PreprintCC BY 4.0arXiv
A Symmetry-First Elementary Derivation of the Lorentz Transformation
Abstract
We present a symmetry-first derivation of the Lorentz transformation in which the speed of light is not imposed at the outset. The argument proceeds in three stages. First, spacetime homogeneity yields additivity, and continuity along free worldlines supplies the passage to linearity. Second, isotropy and the local commutativity of collinear boosts yield velocity reciprocity without assuming it. The first two stages determine a one-parameter family of generalized Lorentz-type transformations. Third, the velocity law, together with the empirical identification of the invariant speed with the coordinate speed of light in vacuum, selects the physical branch, fixes κ=−1/c2, and yields the Lorentz transformation.
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BibTeX
@misc{tan2026symmetryfirst,
title = {{A Symmetry-First Elementary Derivation of the Lorentz Transformation}},
author = {Nianjun Tan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.25159},
eprint = {2605.25159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25159},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Symmetry-First Elementary Derivation of the Lorentz Transformation
AU - Nianjun Tan
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2605.25159
UR - https://arxiv.org/abs/2605.25159
AB - We present a symmetry-first derivation of the Lorentz transformation in which the speed of light is not imposed at the outset. The argument proceeds in three stages. First, spacetime homogeneity yields additivity, and continuity along free worldlines supplies the passage to linearity. Second, isotropy and the local commutativity of collinear boosts yield velocity reciprocity without assuming it. The first two stages determine a one-parameter family of generalized Lorentz-type transformations. Third, the velocity law, together with the empirical identification of the invariant speed with the coordinate speed of light in vacuum, selects the physical branch, fixes κ=−1/c^2, and yields the Lorentz transformation.
ER -